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A survey was given to a random sample of the residents of a town to determine whether they support a new plan to raise taxes in order to increase education spending. The percentage of people who said the supported the plan to raise taxes was 67%. The margin of error for the survey was 3.5%. Write a confidence interval for the percentage of the population that favors the plan.

Question

A survey was given to a random sample of the residents of a town to determine whether they support a new plan to raise taxes in order to increase education spending. The percentage of people who said the supported the plan to raise taxes was 67%. The margin of error for the survey was 3.5%. Write a confidence interval for the percentage of the population that favors the plan.

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Solution

A confidence interval is a range of values, derived from a statistical calculation, that is likely to contain an unknown population parameter. In this case, we are looking for the confidence interval for the percentage of the population that favors the plan to raise taxes for education spending.

The given data is:

  • Sample proportion (p) = 67% or 0.67
  • Margin of error (E) = 3.5% or 0.035

The formula for a confidence interval is:

p ± E

Substituting the given values into the formula, we get:

0.67 ± 0.035

This gives us the confidence interval:

(0.67 - 0.035, 0.67 + 0.035) or (0.635, 0.705)

So, we can be confident that between 63.5% and 70.5% of the population supports the plan to raise taxes for education spending.

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